The statement from the Israeli prime minister's anti-terror office took the unusual step of calling on families of Israelis visiting the Sinai to establish contact with them.

The commander of the anti-terror office, Brig. Gen. Nitzan Uriel, acknowledged that there had been rumors that Israelis have been kidnapped in the Sinai. "We don't work according to rumors," he the Israel TV. "We work according to firm intelligence." He said it would "take some time" to disprove the rumors, which circulated all day Tuesday.

"It is very possible that at this moment, there is a terror cell that has the intention and has a plan in operation to kidnap an Israeli and bring him to Gaza," he said.

Palestinian militants in Gaza have been holding an Israeli soldier captive for more than three years.

Uriel said the kidnappers were likely to strike along the Red Sea coast, a favorite spot for Israelis. "Sinai is a big place," he said, "and it is not impossible to kidnap an Israeli from one of the beaches in the present circumstances."

Uriel told another TV station that about 1,200 Israelis are in Sinai now.

Egyptian police have been searching the Sinai throughout the day for any missing Israelis but found no evidence that anyone was missing, according to two Egyptian security officers speaking under customary conditions of anonymity.

While tens of thousands of Israelis routinely vacation in the Sinai over the Passover holiday, most return after the weeklong festival, which ended a week ago.

In unusually strong wording, the Israeli anti-terror office called "on all Israelis residing in Sinai to leave immediately and return home. Families of Israelis residing in Sinai are asked to contact them and update them on the travel warning."

Israel's anti-terror office has a standing travel advisory telling Israelis to stay out of the Sinai desert because of the threat of terror attacks. However, many Israelis routinely ignore the warning and vacation in the desert and along its Red Sea coast.

In 2004, suicide bombers attacked Egypt's Taba Hilton Hotel, just across the Israeli border, and several campsites where Israelis are known to vacation. Dozens of people were killed and hundreds wounded.

Israel controlled the Sinai from its capture in the 1967 war until returning it to Egypt in 1982 in the framework of a peace treaty between the two nations. The desert is just across the border, and many Israelis flock to the inexpensive seaside resorts nestled at the foot of stark desert mountains — all within driving distance.

The Sinai has been the scene of number of terrorist attacks, including bombings in the resort town of Sharm el-Sheikh in 2005 and Dahab in 2006, which killed dozens. Disgruntled Bedouin influenced by extremist groups were implicated in the attacks.